5,218 research outputs found
One-dimensional weakly nonlinear model equations for Rossby waves
In this study we explore several possibilities for modelling weakly nonlinear
Rossby waves in fluid of constant depth, which propagate predominantly in one
direction. The model equations obtained include the BBM equation, as well as
the integrable KdV and Degasperis-Procesi equations.Comment: 15 page
Mixed finite elements for numerical weather prediction
We show how two-dimensional mixed finite element methods that satisfy the
conditions of finite element exterior calculus can be used for the horizontal
discretisation of dynamical cores for numerical weather prediction on
pseudo-uniform grids. This family of mixed finite element methods can be
thought of in the numerical weather prediction context as a generalisation of
the popular polygonal C-grid finite difference methods. There are a few major
advantages: the mixed finite element methods do not require an orthogonal grid,
and they allow a degree of flexibility that can be exploited to ensure an
appropriate ratio between the velocity and pressure degrees of freedom so as to
avoid spurious mode branches in the numerical dispersion relation. These
methods preserve several properties of the C-grid method when applied to linear
barotropic wave propagation, namely: a) energy conservation, b) mass
conservation, c) no spurious pressure modes, and d) steady geostrophic modes on
the -plane. We explain how these properties are preserved, and describe two
examples that can be used on pseudo-uniform grids: the recently-developed
modified RT0-Q0 element pair on quadrilaterals and the BDFM1-\pdg element pair
on triangles. All of these mixed finite element methods have an exact 2:1 ratio
of velocity degrees of freedom to pressure degrees of freedom. Finally we
illustrate the properties with some numerical examples.Comment: Revision after referee comment
Implementation of the LANS-alpha turbulence model in a primitive equation ocean model
This paper presents the first numerical implementation and tests of the
Lagrangian-averaged Navier-Stokes-alpha (LANS-alpha) turbulence model in a
primitive equation ocean model. The ocean model in which we work is the Los
Alamos Parallel Ocean Program (POP); we refer to POP and our implementation of
LANS-alpha as POP-alpha. Two versions of POP-alpha are presented: the full
POP-alpha algorithm is derived from the LANS-alpha primitive equations, but
requires a nested iteration that makes it too slow for practical simulations; a
reduced POP-alpha algorithm is proposed, which lacks the nested iteration and
is two to three times faster than the full algorithm. The reduced algorithm
does not follow from a formal derivation of the LANS-alpha model equations.
Despite this, simulations of the reduced algorithm are nearly identical to the
full algorithm, as judged by globally averaged temperature and kinetic energy,
and snapshots of temperature and velocity fields. Both POP-alpha algorithms can
run stably with longer timesteps than standard POP.
Comparison of implementations of full and reduced POP-alpha algorithms are
made within an idealized test problem that captures some aspects of the
Antarctic Circumpolar Current, a problem in which baroclinic instability is
prominent. Both POP-alpha algorithms produce statistics that resemble
higher-resolution simulations of standard POP.
A linear stability analysis shows that both the full and reduced POP-alpha
algorithms benefit from the way the LANS-alpha equations take into account the
effects of the small scales on the large. Both algorithms (1) are stable; (2)
make the Rossby Radius effectively larger; and (3) slow down Rossby and gravity
waves.Comment: Submitted to J. Computational Physics March 21, 200
Numerical wave propagation for the triangular - finite element pair
Inertia-gravity mode and Rossby mode dispersion properties are examined for
discretisations of the linearized rotating shallow-water equations using the
- finite element pair on arbitrary triangulations in planar
geometry. A discrete Helmholtz decomposition of the functions in the velocity
space based on potentials taken from the pressure space is used to provide a
complete description of the numerical wave propagation for the discretised
equations. In the -plane case, this decomposition is used to obtain
decoupled equations for the geostrophic modes, the inertia-gravity modes, and
the inertial oscillations. As has been noticed previously, the geostrophic
modes are steady. The Helmholtz decomposition is used to show that the
resulting inertia-gravity wave equation is third-order accurate in space. In
general the \pdgp finite element pair is second-order accurate, so this leads
to very accurate wave propagation. It is further shown that the only spurious
modes supported by this discretisation are spurious inertial oscillations which
have frequency , and which do not propagate. The Helmholtz decomposition
also allows a simple derivation of the quasi-geostrophic limit of the
discretised - equations in the -plane case, resulting in a
Rossby wave equation which is also third-order accurate.Comment: Revised version prior to final journal submissio
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